Do you understand this viral very good math movie clip? (Nathan solves math problem X+Y)

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About the Video

Recently one of you requested that I explain the math(s) in this clip which recently went viral.

https://youtu.be/mYAahN1G8Y8

It's a clip taken from the movie X+Y aka A brilliant young mind. The math(s) problem that Nathan, the main character in this movie, is working on in this clip is a simplified version of the first part of a problem that was shortlisted for the 2009 International Mathematical Olympiad. Here is a link to the shortlist.

https://www.imo-official.org/problems/IMO2009SL.pdf

The problem in question is problem C1 (the number 50 in the problem has been replace by the number 2 in the clip). This problem was suggested to the makers of the movie by Lee Zhao one of the maths consultants of the movie. This Note that the file I've linked to ere also includes solutions...